Advancing Averaged Primer Vector Theory with Bang-Bang Control and Eclipsing
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908839734935552 |
|---|---|
| author | Lifset, Noah |
| author_facet | Lifset, Noah |
| contents | Primer vector theory using averaged dynamics is well suited for optimizing low-thrust, many-revolution spacecraft trajectories, but is difficult to implement in a way that maintains both optimality and computational efficiency. An improved model is presented that combines advances from several past works into a general and practical formulation for minimum-fuel, perturbed Keplerian dynamics. The model maintains computational efficiency of dynamics averaging with optimal handling of the eclipsing constraint and bang-bang control through the use of the Leibniz integral rule for multi-arc averaging. A subtle, but important singularity arising from the averaged eclipsing constraint is identified and fixed. A maximum number of six switching function roots per revolution is established within the averaged dynamics. This new theoretical insight provides a practical upper-bound on the number of thrusting arcs required for any low-thrust optimization problem. Variational equations are provided for fast and accurate calculation of the state transition matrix for use in targeting and optimization. The dynamics include generic two-body perturbations and an expanded state to allow for sensitivity calculations with respect to launch date and flight time. The new model is illustrated on a GTO to GEO transfer, including up to 486 revolutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11660 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Advancing Averaged Primer Vector Theory with Bang-Bang Control and Eclipsing Lifset, Noah Optimization and Control Primer vector theory using averaged dynamics is well suited for optimizing low-thrust, many-revolution spacecraft trajectories, but is difficult to implement in a way that maintains both optimality and computational efficiency. An improved model is presented that combines advances from several past works into a general and practical formulation for minimum-fuel, perturbed Keplerian dynamics. The model maintains computational efficiency of dynamics averaging with optimal handling of the eclipsing constraint and bang-bang control through the use of the Leibniz integral rule for multi-arc averaging. A subtle, but important singularity arising from the averaged eclipsing constraint is identified and fixed. A maximum number of six switching function roots per revolution is established within the averaged dynamics. This new theoretical insight provides a practical upper-bound on the number of thrusting arcs required for any low-thrust optimization problem. Variational equations are provided for fast and accurate calculation of the state transition matrix for use in targeting and optimization. The dynamics include generic two-body perturbations and an expanded state to allow for sensitivity calculations with respect to launch date and flight time. The new model is illustrated on a GTO to GEO transfer, including up to 486 revolutions. |
| title | Advancing Averaged Primer Vector Theory with Bang-Bang Control and Eclipsing |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2505.11660 |